In biotechnological experiments, quantitative analysis of solutions containing biological samples (such as nucleic acids or proteins) is often required. Theoretically, the change of optical intensity (I) is adopted to calculate the optical density (O.D.) of the sample solution having a certain optical path length, i.e., the absorbance (A) of light at a specified wavelength that has passed through the sample solution having the optical path length, which may be expressed as:O.D.=A≡−Log(T)=−Log(I/I0)where A is the absorbance of light having passed through the sample solution, T is the transmittance, and I and I0 denote the intensity of light having passed through the sample solution and a reference solution, respectively. Since the absorbance of light having passed through the solution in a quartz tube of 10-mm in width is conventionally used as a reference, the absorbance converted from the optical intensity as measured is normalized using the Beer-Lambert Law based on the 10-mm standard optical path to obtain the absorbance of light having passed through the sample solution having a 10-mm optical path.
According to the Beer-Lambert Law, the optical intensity of light having passed an absorbing medium by a certain depth weakens because part of the light has been absorbed by the absorbing medium. The optical intensity weakens as the concentration or the thickness of the absorbing medium increases. More particularly, the absorbance is proportional to the optical path length, which may be expresses as:Ax/Ay=Px/Py where A is the absorbance of light having passed through the sample solution, and Px and Py denote the lengths of optical paths x and y, respectively.
The dependence of the solution concentration (c) upon the optical path length P and the absorbance may be expressed as:c=(A×e)/P where e is the wavelength-dependent extinction coefficient. For example, the e value is 50 ng-cm/μL for double-stranded deoxyribonucleic acids (DNA), 33 ng-cm/μL for single-stranded deoxyribonucleic acids, and 40 ng-cm/μL for ribonucleic nucleic acids (RNA). The nucleic acid concentration of the sample solution may be calculated according to the absorbance of the standard optical path length (10 mm) and the e value.
The proteins solution concentration may be calculated according to the Warburg-christian equation:c=(1.55×Aλ=280 nm)−(0.76×Aλ=260 nm)where c is the concentration (mg/ml), A is the absorbance, and λ is the wavelength.
Therefore, the concentration of the sample solution is conventionally calculated based on the relation with the absorbance, which is converted from the optical intensity of light having passed through the solution in a quartz tube. A spectrophotometer may be used for acquiring the transmittance spectrum in a wavelength range from 200 nm to 400 nm. To avoid light from being absorbed by the container during the ultra-violet wavelength range from 200 nm to 400 nm, a quartz tube may be used as the container.
However, such measurement requires a high-cost quartz tube and large volume of sample solution, but shows poor reproducibility and the sample solution cannot be recycledly used. Moreover, the difficulty in cleaning the quartz tube often causes contamination in the sample solution.
Please refer to FIG. 1 to FIG. 3 for cross-sectional diagrams depicting various operation states of a conventional device for quantitative analysis of a nucleic acid solution. In these figures, an optical path is provided in the solution between two fibers due to the adhesion and surface tension of the solution.
The device 10 for quantitative analysis of a nucleic acid solution comprises a stationary arm 14 and a movable arm 12. The stationary arm 14 is provided with a bottom fiber base 147, a solenoid valve 143 and a screw head 141. The bottom fiber base 147 is used to fix a light-emitting fiber 165. The movable arm 12 comprises a magnet 121 disposed at the position corresponding to the screw head 141, a positioning screw 123 disposed at the position corresponding to the solenoid valve 143 and an upper fiber base 127 disposed at the position corresponding to the bottom fiber base 147 for fixing a light-receiving fiber 167.
At a first operation state as shown in FIG. 1, the movable arm 12 and the stationary atm 14 of the device 10 are separated. A nucleic acid solution 18 may be dripped on the bottom fiber base 147 and the light-emitting fiber 165 from a pipet.
Then the movable arm 12 moves downwards so that the positioning screw 123 contacts the plunger 145 in the solenoid valve 143 at a second operation state as shown in FIG. 2. Meanwhile, the upper fiber base 127 and the light-receiving fiber 167 also contact the nucleic acid solution 18. Due to the surface tension and the adhesion of the solution 18, the nucleic acid solution 18 is pulled by the bottom fiber base 147 and the upper fiber base 127 to form a first optical path between the light-emitting fiber 165 and the light-receiving fiber 167. The light emitted from the light source 161 travels through the light-emitting fiber 165 and the nucleic acid solution 18 to enter the light-receiving fiber 167, and is transmitted to the spectrometer 164 for spectrum-dividing and intensity measurement.
The plunger 145 moves downwards as the solenoid valve 143 is turned on. The movable arm 12 moves downwards due to the attractive force between the magnet 121 and the screw head 141 so that the magnet 121 contacts the screw head 141 at a third operation state as sown in FIG. 3. Meanwhile, a second optical path is formed between the light-emitting fiber 165 and the light-receiving fiber 167 even though the nucleic acid solution 18 is compressed.
After the optical intensity in the second optical path has been measured, the optical intensities for the first and the second optical paths are converted into the absorbances. Therefore, the nucleic acid concentration may be calculated according to the Beer-Lambert Law after the absorbance for the standard optical path is obtained by extrapolation.
However, such conventional device 10 for quantitative analysis of a nucleic acid solution comprises a complicated structure. The positioning screw 123 and the screw head 141 that are used for positioning at the second operation state and the third operation state may be loosened due to collision. This causes the variations of the first optical path length and the second optical path length and reduces the precision of the measurement. Accordingly, calibration is required after a certain usage count or a certain period of time, which leads to considerable time cost and maintenance cost.
Moreover, the device 10 for quantitative analysis of a nucleic acid solution is costly because a spectrometer 163 is used for spectrum-dividing and measurement.